4 ms·
An easy way to understand it is by thinking about bunching. Since you're only flipping until you hit the first matching sequence, on average you'll hit the more
by dhbradshaw 11y ago
An easy way to understand it is by thinking about bunching. Since you're only flipping until you hit the first matching sequence, on average you'll hit the more evenly distributed sequence more quickly than the bunched sequence.
Multiple heads in a row are more bunched than transition sequences because, for example, a sequence of three heads in a row will include two sequences with two heads in a row. You can't do that with a transition sequence--it takes at least four tosses to get two identical transition sequences.
- JoshCole 11y agoYour explanation actually confused me until I realized we can't conflate the two different players' throws. We basically have four cases for Bob: - HH: terminates for Bob. - HT: Bob restarts the sequence. - TT: Bob restarts the sequence. - TH: This is a continuation. It degenerates into the answer to a single throw. Otherwise its just a recursion. Then we have another four cases for Alice: - HH: This is a continuation. It degenerates into the answer to a single throw or else a recursion. - HT: terminates for Alice. - TT: Alice restarts the sequence. - TH: This is a continuation. It degenerates into the answer to a single throw. Otherwise its just a recursion. So with that understanding it is a bit more clear how we get this result: Alice has one win and two opportunities for a win and one for a restart. Bob has one win and one opportunity for a win and two restarts. That was a bit confusing. I wonder how the problem could be worded to ensure that people got the answer correctly every time?